An existence principle for nonlocal difference boundary value problems with -Laplacian and its application to singular problems.
An existence result for a multipoint boundary value problem on a time scale.
An expanded class of parametric partial linear complex vector functional equations.
An extension theorem.
An extension theorem for a Matkowski-Sutô problem
Let I be an interval, 0 < λ < 1 be a fixed constant and A(x,y) = λx + (1-λ)y, x,y ∈ I, be the weighted arithmetic mean on I. A pair of strict means M and N is complementary with respect to A if A(M(x,y),N(x,y)) = A(x,y) for all x, y ∈ I. For such a pair we give results on the functional equation f(M(x,y)) = f(N(x,y)). The equation is motivated by and applied to the Matkowski-Sutô problem on complementary weighted quasi-arithmetic means M and N.
An extremal problem related to probability.
An improvement of the Grüss inequality.
An inconsistency equation involving means
We show that any quasi-arithmetic mean and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations and are the constant ones.
An initial value problem for a functiona equation.
An inverse problem for the discrete periodic Schrödinger operator.
An Odd Solution to the Functional Equation ... = exp (P(x)).
An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations
We establish an optimal, linear rate of convergence for the stochastic homogenization of discrete linear elliptic equations. We consider the model problem of independent and identically distributed coefficients on a discretized unit torus. We show that the difference between the solution to the random problem on the discretized torus and the first two terms of the two-scale asymptotic expansion has the same scaling as in the periodic case. In particular the L2-norm in probability of the H1-norm...
An ultradiscrete matrix version of the fourth Painlevé equation.
Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order
Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) = λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 = 0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) + αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R, n = 0, 1, 2, . . ., α−1 = α−2...
Analogies between differential equations: Singular solutions of difference equations of Clairaut's type.
Analogs of Bernoulli polynomials in fields Zp.
Analytic roots of invertible matrix functions.
Analytic solutions for polynomial-like iterative equations with variable coefficients
Analytic solutions of polynomial-like iterative functional equations with variable coefficients are discussed in the complex field ℂ by reducing to an auxiliary equation and by applying known results for systems of nonlinear functional equations of finite orders.
Analytic solutions of a nonlinear two variables difference system whose eigenvalues are both 1
For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations: ⎧ x(t+1) = X(x(t),y(t)) ⎨ ⎩ y(t+1) = Y(x(t), y(t)) where , satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂| ≠ 1" or "μ...
Analytic solutions of Böttcher's functional equation in the unit disk.